Related papers: Random Iteration of Cylinder Maps and diffusive be…
We explore the probability that a permutation sampled from the symmetric group of order n uniformly at random has cycles of lengths not exceeding r. Asymptotic formulas valid in specified regions for the ratio n/r are obtained using the…
We consider uniform random permutations of length $n$ conditioned to have no cycle longer than $n^\beta$ with $0<\beta<1$, in the limit of large $n$. Since in unconstrained uniform random permutations most of the indices are in cycles of…
Voiculescu's notion of asymptotic free independence applies to a wide range of random matrices, including those that are independent and unitarily invariant. In this work, we generalize this notion by considering random matrices with a…
We consider random Hermitian matrices made of complex or real $M\times N$ rectangular blocks, where the blocks are drawn from various ensembles. These matrices have $N$ pairs of opposite real nonvanishing eigenvalues, as well as $M-N$ zero…
Let $\mathcal{T}_n$ be the set of all mappings $T:\{1,2,\ldots,n\}\to\{1,2,\ldots,n\}$. The corresponding graph of $T$ is a union of disjoint connected unicyclic components. We assume that each $T\in\mathcal{T}_n$ is chosen uniformly at…
We consider properties of determinants of some random symmetric matrices issued from multivariate statistics: Wishart/Laguerre ensemble (sample covariance matrices), Uniform Gram ensemble (sample correlation matrices) and Jacobi ensemble…
In the paper [25], written in collaboration with Gesine Reinert, we proved a universality principle for the Gaussian Wiener chaos. In the present work, we aim at providing an original example of application of this principle in the…
Let $A$ be an $n\times n$ random matrix with independent rows $R_1(A),\dots,R_n(A)$, and assume that for any $i\leq n$ and any three-dimensional linear subspace $F\subset {\mathbb R}^n$ the orthogonal projection of $R_i(A)$ onto $F$ has…
We explore the limiting empirical eigenvalue distributions arising from matrices of the form \[A_{n+1} = \begin{bmatrix} A_n & I\\ I & A_n \end{bmatrix} , \]where $A_0$ is the adjacency matrix of a $k$-regular graph. We find that for…
We apply Tsallis's q-indexed entropy to formulate a non-extensive random matrix theory (RMT), which may be suitable for systems with mixed regular-chaotic dynamics. The joint distribution of the matrix elements is given by folding the…
In this article, we attempt to study the possible link between the dynamics of a circle map and the caustics of its iterations. The attention is on a geometrically defined off-center reflections, which, coincidentally, is also a…
We explore some of the connections between the local picture left by the trace of simple random walk on a discrete cylinder with base a d-dimensional torus, d at least 2, of side-length N running for times of order N^{2d} and the model of…
In this paper we deal with the classical problem of random cover times. We investigate the distribution of the time it takes for a Poisson process of cylinders to cover a set $A \subset \mathbb{R}^d.$ This Poisson process of cylinders is…
This paper concentrates on asymptotic properties of determinants of some random symmetric matrices. If B_{n,r} is a n x r rectangular matrix and B_{n,r}' its transpose, we study det (B_{n,r}'B_{n,r}) when n,r tends to infinity with r/n \to…
The objective of this paper is to examine the asymptotic behavior of persistence diagrams associated with \v{C}ech filtration. A persistence diagram is a graphical descriptor of a topological and algebraic structure of geometric objects. We…
Single partially confined collapsed polymers are studied in two dimensions. They are described by self-avoiding random walks with nearest-neighbour attractions below the $\Theta$-point, on the surface of an infinitely long cylinder. For the…
One way to model telecommunication networks are static Boolean models. However, dynamics such as node mobility have a significant impact on the performance evaluation of such networks. Consider a Boolean model in $\mathbb{R}^d$ and a random…
Analytically tractable dynamical systems exhibiting a whole range of normal and anomalous deterministic diffusion are rare. Here we introduce a simple non-chaotic model in terms of an interval exchange transformation suitably lifted onto…
Let $r=r(n)$ be a sequence of integers such that $r\leq n$ and let $X_1,\ldots,X_{r+1}$ be independent random points distributed according to the Gaussian, the Beta or the spherical distribution on $\mathbb{R}^n$. Limit theorems for the…
For $i = 0, 1, \ldots, n$, let $C_i$ be independent and identically distributed random variables with distribution $F$ with support $(0,\infty)$. The number of zeros of the random tropical polynomials $\mathcal{T}f_n(x) =…